What kind of lawyer do I need to sue cable company?

Get a consumers rights attorney. If you can show that the cable company does this as a matter of policy to many customers, you could have a large class action case on your hands. Otherwise, a suit under consumer fraud would be the way to get your overcharge back.

Any attorney who understands the limits to liability of the cable companies and the rules regrding telecommunications franchises and the NYS regulatory system of such licensees should be able to help competently.

You don't say what the basis for the overcharge is. If it is something that the cable company is likely overcharing everyone, I suggest you look for an attorney who specializes in class action law suits.